「20 16」 SEM 2

STUDIO AIR

_____________________________________________ SERENA YU TUTOR: MATTHEW MCDONNELL

ALGORITHMIC SKETCHBOOK

___________________________________________

CONTENTS 4

6

7

8

9

10

14

NOTES AND GRASSHOPPER WORK

USING DATA INFORMATION ON GRASSHOPPER

LONGEST LIST, SHORTEST LIST AND CROSS REFERENCE TO CONNECT POINTS

END POINTS

EVALUATE CURVE

LOFTING

EXTRUDE

21

22

23

24

29

32

PFRAME, POLYGON AND SERIES

CREATING PATTERNS ON SPHERES

USING METABALL

EXTRUDING CONTOURS

IMAGE SAMPING

MAKING A GRIDSHELL

CREATING SPIRALLING FORMS

34

35

36

37

38

40

42

USING CULLING FUNCTION ON VORONOI

USING BOXS MORPH ON SOLIDS

CREATING A PATTERNED SOLID

CREATING COLOURED SHAPES ON GRIDS

CREATING PATTERENED PLANES AROUND CIRCLE

KANGAROOPLUG-IN NOTES

CREATING DRAPES WITH KANGAROO PLUG-N

44

45

46

48

49

50

51

MANIPULATING PLANE POSITIONS WITH CURVED LINE AS ITS REFERENCE

CREATING SPIRALS WITH THE USE OF THE PIPE FUNCTION

USING THE PIPE FUCNTION ON CLOSED POLYGONS

USING WEAVERBIRD PLUG-IN TO CREATE SIDES ON MESHES

KANGAROO PLUG-IN TO CREATE PLATES ON SURFACE OF SPHERE

CREATING CONES BY CULLING CURVES

CREATING ARCS ON GRIDS

52

53

54

56

58

60

66

CREATING DIFFERENT SIZES OF CIRCLES WITH ATTRACTOR POINTS ON GRID

CREATING CONES ON SQUARE GRID AND MANIPULATING CONE SIZE WITH GRAPH MAPPER

MANIPULATING SHAPE OF VORONOI FRAME

CREATING EXTTRUDED PANELS WITH LUNCHBOX PLUG-IN ON CURVED LINES

CREATING FRAMES ON POLYLINES WITH WEAVERBIRD PLUG-IN

SMALL EXPERIMENTS WITH THE CONE COMPONENT

LOFTING AND EXTRUDING THE SURFACE WITH VECTORS

16

CONTENTS 68

70

72

74

76

88

92

FAILED ALGORITHM THAT PRODUCED NO OUTCOME

CREATING TOWERS BASED ON A RECTANGLE COMPONENT

CREATING FRAMES BASED ON IMAGE DATA

HANDWRITTEN NOTES

BASICS

IMAGE SAMPLING

VECTORS

98

108

116

USING AND MANIPULATING DATA IN GRASSHOPPER

USING EXPRESSIONS AND THE MATH MENU

MAKING PHYSICAL MODELS

NOTES AND GRASSHOPPER WORK

PAGE 4

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USING DATA INFORMATION ON GRASSHOPPER Flatten Tree: You flatten a tree to reconstruct the data in the tree structure. This is done by deleting the branch and putting that data under the root of the data tree.

Graft Tree: This is used to reconstruct the data of a tree structure too. But it is done by addiing a branch to each data item. It is different to flattening but it can be used in combination with it too. To graft a tree, firstly, delete the original branch. The data items at the root will then be on a new branch.

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LONGEST LIST SHORTEST LIST AND CROSS REFERENCE TO CONNECT POINTS

Longest list definition

Longest list connects points to lines until all points are connected

Shortest list definition

Shortest list connects points to lines until one curveâ€™s points run out

Cross reference definition

Cross reference makes all possible connections between points

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END POINTS

The ‘end point component’ defines the ends of a curve with points. The end point can be useful when you want to connect the ends of two curves together. The definition below shows how you can extract end points out of cuves and connect them together via the ‘line’ components.

This is what the component looks like

Defintion to connect two curves

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End result of the definition

EVALUATE CURVE

The ‘evaluate curve’ component can be used to define a particular location of a curve. There two methods to do this and they both give the same result Method 1: The first method involves right clicking on the ‘curve’ component then selecting ‘reparamatise’/ If you do this the slider should be set to be from 0-1 as the the units of the curve is reparamatised to have values from 0-1. Therefore, after it is reparamatised 0.5 means the mid way point of the curve, 0 is the start,a nd 1 is the end point. Method 2: This method is to not reparamatise it. If you don’t reparamatise it the slider value is dependent on the actual numerical unit of the length of the curve. So if the slider unit is set at 0.5 in this case the point would be 0l.5 units upwards from the start of the curve.

This is what the component looks like

Defintion for Method 1

This is what the point of the curve looks like

Defintion for Method 2

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LOFTING

To loft curves you just need to reference the curves from Rhino onto Grasshopper. Referencing multiple curves can be done in two ways: - The first way is shown through the Grasshopper definition at the top from the left page. You right click and select ‘refernce multiple curves’ to compile all the curves onto one component. This method is the most convenient. - The way is to reference each curve from Rhino individually to each curve component on Grasshopper. You have to hold onto the ‘shift’ button on the keyboard to allow multiple inputs on the ‘loft’ component. Overall, this way to do it is more time consuming but it is useful if you want to manipulate each lofted area from a particular curve uniquely. To alter the form of the loft press ‘F10’ on the keyboard to have the points of the curve displayed on the screen. Click on the points and move it around to change the loft form. So far the loft only exists on Grasshopper even though it is displayed on the Rhino screen. This is why you cannot select the loft on Rhino with your mouse. To have the loft on Rhino select the entire definition, right click, the choose ‘bake’. After it is baked the loft is not physically present in Rhino.

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1. Create curves on Rhino and reference them on Grasshopper

2. Loft curves with ‘loft’ component on grasshopper

3. (Optional) Press ‘F10’ to display points on the curve.

4. (Optional) To change the form of the curve, move the points.

5. Bake the Grasshopper definition to have it on Rhino.

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LOFTING

EXTRUDE

The extrusion example on the right utilises an ‘offset’ component to have many sets of curves offsetted at once when there was only a singular set of curves to begin with. The ‘extrusion’ component requires a ‘vector’ component to be present in order for it to extrude towards a particular directionl. There are 3 different types of vectors: Unit Z - Directs the extrusion along the z axis Unit Y - Directs the extrusion along the y axis Unit X - Directs the extrusion along the x axis

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USING THE ‘EXTRUDE’ COMPONENT ON MULTIPLE CURVES

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PFRAME, POLYGON AND SERIES

Pframe: The ‘pframe’ component creates perpendicular frames on a curve. Polygon: The polygon component allows users to create polygons of a shape. The component inlcudes the manipulation of the polygon’s base plane, radius, number of sides and the curviness of its corners. Series The ‘series’ component evenly spaces certain elements. Example of using the the combination of the 3 to create panels based on the shape of a curve: Create perpendicular frames on a curve >> Create polygons of a certain shape aligned perpendicularly by relying on the ‘Pframe’ component’ >> Evenly space the polygons with a ‘Series’ component

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MANIPULATING PLANE POSITION WITH ‘SERIES’

PAGE 18

MANIPULATING PLANE POSITION WITH ‘SERIES’

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MANIPULATING PLANE POSITION WITH ‘SERIES’

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CREATING PATTERNS ON SPHERES

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USING ‘METABALL’

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EXTRUDING CONTOURS

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IMAGE SAMPLING

Notes for using circles based on image data to create a picture with circles of the same picture: - The ‘Sdivide’ component create a grid of points on a surface. These points form the location of where the circles will be located at. Must remmeber to right click on the ‘S’ input of the component and select ‘reparamatise’. This is so that the points resign within the space form 0-1. The reason for this is because the ‘image sampler’ is det on default to take the values 0-1 on the x and y axis. Therefore, for the ‘Sdivide’ and ‘image sampler’ to work together the ‘Sdivide must be reparamatised. - For the ‘image sampler’ it on default uses the values 0-1 to quantify its image data. In which, black has a value of 1, white a value of 0 and grey a value between 0-1. The bigger the value the bigger the size of the circle. - There is an ‘expression’ component before the circles. This expression component says: (x*y)+0.1. The 0.1 defines the minimum size for the circle so there are circles everywhere on the surface. White has a value of 0 but with this expression you’ll see a circle deifned to a size of 0.1 units and not 0 which means no circle at all. But you can change that number to any number, the value 0.1 is only used as an example in this case.

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THE TOP ARE THE NOTES FOR DEFINITONFOR USING ONE IMAGEâ€™S DATA. THE BOTTOM ARE THE NOTES FOR LAYERING IMAGE DATA TOGETHER.

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LAYERING ONE IMAGEâ€™S DATA OVER ANOTHER

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‘IMAGE SAMPLING’ ON SURFACES

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MAKING A GRID SHELL

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MAKING A GRID SHELL WITH UNSUAL GEOMETRIES AND USING THE ‘PIPE’ COMPONENT

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CREATING SPIRALLING FORMS

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USING ‘CULLING’ FUNCTION ON ‘VORONOI’

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USING ‘BOX MORPH’ ON SOLIDS

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CREATING A PATTERNED SOLID

PAGE 36

CREATING COLOURED SHAPES ON GRIDS

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CREATING PATTERNED PLANES AROUND CIRCLE

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KANGAROOâ€™ PLUG-IN NOTES

Kangaroo cn be used to self organise structures by manipulating its forces of attraction and repulsion. The following are examples of what kangaroo can do:

Springs (run on sets of 2 particles): Force particles - if the forces between two particles are repulsive at short distances but attractive at long distances the particles will settle at the distance where the force is zero - this is used to cause a set of particles to self organise. Equalisation (run on sets of 2 particles): Measure the lengths of a set of lines, find the average, then treat those lines as springs with this average as their rest length. Planarisation: Get the shorest vector between the diagonals of a quadrilateral, and use it to pull the top two vertices down, and the bottom two up. This causes it to become planar. Bending (runs on a set of three particles): If you apply a force from the central vertex towards the average of its two neighbours, there is half the oppsite force to the neighbours. this creates bending.

PAGE 40

Circularisation: To see if a shape is a perfect sphere of circle first place O randomly inside the shape in kangaroo. Then equalise the radial lines and planarise it. O is then siutated in the middle of the shape and A, B, C and are on the edge of the shape. If OA, OB, OC and OD have equal lengths then A, B, C and D lie on a common sphere. If ABCD is planar it can also mean that they lie on a common circle.

In this case the shape on the left is a perfect circle but the shape on right is not. This is because OA, OB, OC and PD are only of equal lengths on the left.

CP Meshes: If the sum of the lengths of the opposite edges of a quad made of two triangles are equal then the triangles have tangent incircles. In meshes if all adjacent triangles have equal opposite edge lengths for tangent incircles then this is called ‘circle packing’ or ‘CP’ meshes. Having tangent circles within the individual triangles mean that the geometry can form a very structurally stable construction with torsion free beam layouts.

If the oppsite lengths of a the triangles are the same you can make tangent insircles within them. Such form is very structurally stable.

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CREATING DRAPES WITH KANGAROO PLUG-IN

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PAGE 43

MANIPULATING PLANE POSITIONS WITH A CURVED LINE AS ITS REFERENCE

PAGE 44

CREATING SPIRALS WITH THE USE OF THE ‘PIPE’ COMPONENT

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USING THE PREVIOUS ‘PIPE’ FUNCTION ON CLOSED POLYGON SHAPES

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USING ‘WEAVERBIRD’ PLUG-IN TO CREATE SIDES ON MESHES

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USING ‘KANGAROO’ PLUGIN TO CREATE PLATES ON SURFACE OF SPHERE FACING DIFFERENT DIRECTIONS

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CREATING CONES BY CULLING CURVES

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CREATING ARCS ON GRID

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CREATING DIFFERENT SIZES OF CIRCLES WITH ATTRACTOR POINTS ON GRID

PAGE 52

CREATING CONES ON SQUARE GRID AND MANIPULATING CONE SIZE WITH ‘GRAPH MAPPER’

PAGE 53

MANIPULATING SHAPE OF VORONOI FRAME

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CREATING EXTRUDED PANELS WITH ‘LUNCHBOX’ PLUG-IN ON CURVED LINES (NOTE: IT DOES NOT PRODUCE OFFSETTED PANELS EFFECT WITH STRAIGHT LINES)

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CREATING FRAMES ON POLYLINES WITH ‘WEAVERBIRD’ PLUG-IN

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PAGE 59

EXPERIMENTING WITH THE ‘CONE’ COMPONENT: I TRIED TO USE IMAGE SAMPLING WITH THIS DEFINTION TO CHANGE THE LOCATION OF THE POINTS ON THE INTERPOLATED CURVES BUT IT YEILED NO VISIBLE RESULTS

PAGE 60

EXPERIMENTING WITH THE ‘CONE’ COMPONENT: THE CIRCLES PRODUCED A VERY INTERESTING MESH EFFECT. THE PICTURE ON THE LEFT IS THE WHOLE DEFINTION BAKED AND THE IMAGE ON THE RIGHT HAS ONLY THE CIRCLES BAKED

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EXPERIMENTING WITH THE ‘CONE’ COMPONENT: THIS CREATE A WEIRD LOFT ON THE BASE OF THE CONES, POSSIBLY DERIVED FROM THE POINTS GENERATED BY ‘POP 2D’

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EXPERIMENTING WITH THE ‘CONE’ COMPONENT: I USED THE ‘PIPE COMPONENT HERE. THE IMAGE ON THE LEFT HAS ONLY THE ‘PIPE’ BAKED AND THE IMAGE ON THE RIGHT HAS THE WHOLE DEFINITION BAKED

PAGE 63

EXPERIMENTING WITH THE ‘CONE’ COMPONEN: THE INTERPOLATED CURVES ARE LIFTED UP WITH A ‘UNIT Z’ VECTOR. WHEN I TRIED TO LOFT THE LEFTED AREAS NOTHING HAPPENED AND IT MIGHT BE BECAUSE IT’S COMPOSED OF ONLY ONE CURVE AND THE CURVE IS TOO COMPICATED TO LOFT WITH

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EXPERIMENTING WITH THE ‘CONE’ COMPONENT: I ADDED ‘VORONOI’ TO THE ‘INTERPOLATED CURVE AND IT GAVE A VERTICAL FRAME THAT GOES THROUGH THE CONES

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LOFTING AND EXTRUDING THE SURFACE WITH VECTORS

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FAILED DEFINTION OF USING IMAGE SAMPLING TO CREATE CURVED FRAMES IT'S THE 'DECONSTRUCT MESH' THAT BECAME A RED BOX FIRST SO IT MEANS THAT THE DEFINITION STARTED TO BECOME INVALID FROM THERE. THE FOLLOWING ARE THE REASON FOR WHY I THINK THE DEFINITION FAILED: -THE START OF THE DEFINTION WASN'T A MESH SO I WASN'T ABLE TO USE 'DECONSTRUCT MESH' -THE 'IMAGE SAMPLING' DIDN'T PRODUCE DATA THAT IS SUITABLE FOR THE 'DECONSTRUCT MESH' TO CREATE POINTS WITH -THE 'IMAGE SAMPLING' WAS NOT ABLE TO CONVERT THE 'SURFAE DIVIDED POINTS' IN A SIMPLE WAY

PAGE 68

ATTEMPT 2 I TRIED TO CONNECT THE 'IMAGE SAMPLING' WITH THE INTEROPLATED CURVES THIS TIME AND THE RED ON THE 'DECONSTRUCT MESH' DISSAPEARED. BUT THE OTHER COMPONENTS ARE STILL IN ORANGE AND IT SAYS THAT THEY CANNOT READ THE DATA INPUT. I TRIED FLATTENING, SIMPLIFYING, REPARAMATISING AND GRAFTING TO REARRANGE THE DATA ON THE 'INTERPOLATED CURVE' BUT IT STILL DIDN'T WORK.

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CREATING TOWERS BASED ON A 'RECTANGLE' COMPONENT

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CREATING FRAMES BASED ON 'IMAGE DATA NOTE: I ONLY BAKED THE END OF THE DEFINITION FOR THE FRAME STRUCTURE

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HANDWRITTEN NOTES

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BASICS

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INTRODUCTION TO SURFACE POINTS

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CREATING A GRIDSHELL WITH ARCS

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MORE ON HOW TO CREATE THE STRUCTURE OF A GRIDSHELL

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HOW TO LOFT ARCS COMPLETELY WITHOUT GAPS

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NOTES ABOUT INDIVIDULA COMPONENTS USEFUL FOR PATTERNING

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NOTES ON CREATING LINES, LOFTING BI-ARCS AND THE SHORTCUT TO NAMING TEXT PANELS

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BASICS ON GRASSHOPPER

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BASICS ON BREP EDGES, LOFTING AND TRIANGULATION ALGORITHMS

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CURVE MENU NOTES

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CURVE MENU NOTES

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IMAGE SAMPLING

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BASIC DEFINITION FOR USING IMAGE SAMPLING ON A SURFACE

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USING IMAGE SMAPLING ON BREPS

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VECTORS

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VECTOR FUNDAMENTALS

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EVALUATING FIELDS

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FIELD FUNDAMENTALS

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VISUALISING FIELDS WITH A ‘TENSOR DISPLAY’

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USING AND MANIPULATING DATA IN GRASSHOPPER

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RANGE, DOMAIN AND POINTS

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PATTERNING LISTS

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CREATING A GRID OF POINTS

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TREE MENU

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TREE DIMENSIONS

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TREE STATISTICS VISUALISATION

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WHAT A DATA TREE IS

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USING EXPRESSIONS AND THE MATH MENU

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COMPONENTS THAT ARE USEFUL IN COMBINATION WITH EXPRESSIONS

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PHYLIOTAXIS EXPRESSION

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TO CREATE THE PHYLIOTAXIS

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INTRODUCTION TO SPIRALS

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CREATING A SPIRAL

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HOW DIFFERENT COMPONENTS CREATES DIFFERENT TYPES OF SPIRALS

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MAKING PHYSICAL MODELS

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CREATING JOINTS

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